Error Estimates for Advanced Galerkin Methods / by Marcus Olavi Rüter.

Format:

Book

Author/Creator:

Rüter, Marcus Olavi, author.

Contributor:

SpringerLink (Online service)

Series:

Engineering (Springer-11647)

Lecture notes in applied and computational mechanics 1613-7736 ; 88.

Lecture Notes in Applied and Computational Mechanics, 1613-7736 ; 88

Language:

English

Subjects (All):

Mechanics.

Mechanics, Applied.

Computer science--Mathematics.

Computer science.

Computational intelligence.

Solid Mechanics.

Computational Science and Engineering.

Computational Intelligence.

Local Subjects:

Solid Mechanics.

Computational Science and Engineering.

Computational Intelligence.

Physical Description:

1 online resource (XIV, 496 pages) : 766 illustrations, 179 illustrations in color.

Edition:

First edition 2019.

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2019.

System Details:

text file PDF

Summary:

This monograph provides a compendium of established and novel error estimation procedures applied in the field of Computational Mechanics. It also includes detailed derivations of these procedures to offer insights into the concepts used to control the errors obtained from employing Galerkin methods in finite and linearized hyperelasticity. The Galerkin methods introduced are considered advanced methods because they remedy certain shortcomings of the well-established finite element method, which is the archetypal Galerkin (mesh-based) method. In particular, this monograph focuses on the systematical derivation of the shape functions used to construct both Galerkin mesh-based and meshfree methods. The mesh-based methods considered are the (conventional) displacement-based, (dual-)mixed, smoothed, and extended finite element methods. In addition, it introduces the element-free Galerkin and reproducing kernel particle methods as representatives of a class of Galerkin meshfree methods. Including illustrative numerical examples relevant to engineering with an emphasis on elastic fracture mechanics problems, this monograph is intended for students, researchers, and practitioners aiming to increase the reliability of their numerical simulations and wanting to better grasp the concepts of Galerkin methods and associated error estimation procedures.

Contents:

Introduction

Newtonian and Eshelbian Mechanics

Boundary Value Problems

Galerkin Methods

Numerical Integration

Energy Norm A Posteriori Error Estimates

Goal-oriented A Posteriori Error Estimates in Linearized Elasticity

Goal-oriented A Posteriori Error Estimates in Finite Hyperelasticity

Numerical Examples

The Nonstandard Dyadic Product Operators

Push-forward and Pull-back Operations

Tensor derivatives

A Generalized Nitsche Method

The J-integral in Elastic FractureMechanics

Linearizations

Materials investigated in this monograph

Functional Analysis-A Synopsis.

Other Format:

Printed edition:

ISBN:

978-3-030-06173-9

9783030061739

OCLC:

1127287097

Access Restriction:

Restricted for use by site license.